Question

Derive an expression for time period of conical pendulum.​

Answer 1

Answer:

Fc = T sin theta  = m v^2 / (L sin theta)      T = tension and Fc = centripetal force

Fg = T cos theta = m g        gravitational component of T

cot theta = g L sin theta / v^2    dividing equations

v^2 = 4 pi^2 f^2  L^2 sin^2 theta = = 4 pi^2 L^2 sin^2 theta / P^2

where P = period

cot theta = g L sin theta P^2 / (4 pi^2 L^2 sin^2 theta)

cot theta = g P^2 / (4 pi^2 L sin theta)

P^2 = 4 pi^2 L cos theta / g

P = 2 pi (L cos theta / g)^1/2